Chapter 1: Matter, Measurement, and Problem Solving – Study Notes

Chapter 1: Matter, Measurement, and Problem Solving

Introduction to Matter

Matter is the foundation of chemistry and is defined as anything that occupies space and has mass. The properties of matter are determined by the nature and arrangement of its atoms and molecules.

• Matter: Anything that occupies space (has volume) and possesses mass.

• Properties of Matter: Determined by the properties and arrangement of atoms and molecules within the substance.

• Example: Water molecules (H2O) have different properties than carbon dioxide molecules (CO2).

Key Definitions

Understanding chemistry requires familiarity with several foundational terms.

• Atom: The smallest particle of an element, retaining its unique chemical characteristics.

• Molecule: A collection of atoms chemically bonded together in fixed proportions and arrangements.

• Chemistry: The science that studies the behavior of matter by examining atoms and molecules.

The Scientific Approach

Chemistry relies on a systematic method for investigating phenomena and developing scientific knowledge.

• Hypothesis: A tentative explanation for a set of observations.

• Scientific Law: A statement that summarizes past observations and predicts future ones (describes what happens).

• Scientific Theory: A general explanation of widely observed phenomena that has been extensively tested (explains why it happens).

• Example:

  • Law of Conservation of Mass (Lavoisier): In a chemical reaction, mass is neither created nor destroyed. $\text{Total mass remains constant}$

  • Dalton's Atomic Theory: Matter is composed of small, indestructible particles called atoms. During chemical reactions, atoms are rearranged, not created or destroyed.

States of Matter

Matter exists in different physical states, each with distinct properties.

• Gas: Variable shape and volume.

• Liquid: Fixed volume, changeable shape.

• Solid: Fixed shape and volume.

Crystalline vs. Amorphous Solids

Solids can be classified based on the arrangement of their atoms or molecules.

• Crystalline Solid: Atoms/molecules arranged in a long-range, repeating order (e.g., diamond, salt, sugar).

• Amorphous Solid: No long-range, repeating order (e.g., glass, most plastics).

Classes of Matter

Matter can be categorized as pure substances or mixtures.

• Pure Substance: Contains only one chemical.

  • Element: Simplest matter, only one kind of atom (e.g., copper).

  • Compound: Two or more elements bonded together in a fixed composition (e.g., H2O).

• Mixture: Contains two or more chemicals.

  • Homogeneous Mixture: Uniform composition (e.g., black coffee).

  • Heterogeneous Mixture: Non-uniform composition (e.g., air in a room, pencil).

Separating Mixtures

Mixtures can be separated based on differences in physical properties, without breaking chemical bonds.

• Filtration: Separates solids from liquids using a filter (e.g., gravity filtration).

• Distillation: Separates liquids based on differences in boiling points.

• Paper Chromatography: Separates substances based on their preference for stationary vs. mobile phases.

Physical vs. Chemical Properties

Properties of substances are classified as physical or chemical.

• Physical Properties: Characteristics observed without changing the substance (e.g., hardness, color, melting point).

• Chemical Properties: The tendency of a substance to undergo a chemical reaction with another substance (e.g., iron reacts with oxygen to form rust).

Energy in Chemistry

Energy is central to chemical and physical changes.

• Energy: The capacity to do work.

• Work: Force acting through distance.

• Types of Energy:

  • Kinetic Energy: Associated with motion.

  • Thermal Energy: Associated with temperature (particle motion).

  • Potential Energy: Associated with position or composition.

• Law of Conservation of Energy: Energy can be converted from one form to another, but cannot be created or destroyed. $\text{Total energy is constant}$

Making Measurements

Accurate and precise measurements are essential in scientific experimentation.

• Accurate Measurements: Essential for reliable data.

• Standardized Units: Needed for sharing and comparing data.

• Error Analysis: Crucial for interpreting experimental results.

SI Base Units

The International System of Units (SI) provides standardized units for scientific measurements.

Quantity	Unit Name	Unit Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin	K
Energy	Joule	J
Amount of Substance	Mole	mol
Electrical Current	Ampere	A
Luminosity	Candela	cd

Prefixes for SI Units

SI units use prefixes to indicate multiples or fractions of base units.

Name	Symbol	Multiplier	Exponential
tera	T	1012	1012
giga	G	109	109
mega	M	106	106
kilo	k	103	103
deci	d	10-1	10-1
centi	c	10-2	10-2
milli	m	10-3	10-3
micro	μ	10-6	10-6
nano	n	10-9	10-9
pico	p	10-12	10-12

Temperature Scales

Temperature is measured using different scales, with conversions based on linear relationships.

• Celsius (°C), Fahrenheit (°F), Kelvin (K): Common temperature scales.

• Absolute Zero: The temperature at which all motion stops.

• Conversion Equations:

  • $T_{°F} = 1.8 \times T_{°C} + 32$

  • $T_K = T_{°C} + 273.15$

English-Metric Conversions

Conversions between English and metric units are essential in scientific calculations.

• 1 in = 2.54 cm (exact)

• 1 lb = 453.592 g

• 1 gal = 3.7854 L

• 1 mL = 1 cm3 (by definition)

Derived Units: Volume & Density

Some quantities are derived from base units.

• Volume: $(\text{unit of length})^3$

• Density: Mass per unit volume. Can be used as a conversion factor.

  • $\text{density} = \frac{\text{mass}}{\text{volume}}$

  • $d = \frac{m}{V}$

Extensive vs. Intensive Properties

Properties of matter are classified based on their dependence on the amount of substance.

• Extensive Property: Varies with the amount of substance (e.g., length, mass, volume).

• Intensive Property: Independent of the amount of substance (e.g., color, density, melting point).

Precision and Accuracy

Measurement quality is assessed by precision and accuracy.

• Precision: Repeatability of measurements and their agreement with each other.

• Accuracy: Agreement between experimental value and the true value.

Sources of Error

Errors in measurement can be random or systematic.

• Random Errors: Result from limitations of the instrument (e.g., scale reading fluctuations). Associated with precision.

• Systematic Errors: Result from faulty instrumentation or experimental design (e.g., miscalibrated thermometer). Associated with accuracy.

Experimental Measurements & Significant Figures

Measurements always have some degree of uncertainty, which is reflected in significant figures.

• Uncertain Digit: The digit that must be estimated in a measurement.

• Significant Figures: All certain digits plus the uncertain digit.

• Counting Significant Figures:

  • Nonzero integers are always significant.

  • Leading zeros are not significant.

  • Interior zeros (between nonzero digits) are significant.

  • Trailing zeros (after decimal point) are significant.

  • Trailing zeros (without decimal point) are not significant.

Rule	Example	Number of Significant Figures
Nonzero digits	123.45	5
Leading zeros	0.045	2
Interior zeros	101	3
Trailing zeros (decimal)	100.0	4
Trailing zeros (no decimal)	100	1

Exact Numbers

Exact numbers have an infinite number of significant figures and arise from definitions or counting.

• Examples: 1 inch = 2.54 cm (exact), 1 km = 1000 m, 1 dozen = 12 items, 1 hour = 60 minutes, 1 H2O molecule = 2 H atoms.

Significant Figures in Calculations

Rules for handling significant figures differ for addition/subtraction and multiplication/division.

• Addition/Subtraction: Round to the first column with an uncertain digit (largest error).

• Multiplication/Division: Round to the same number of significant figures as the smallest number in any factor.

Conversion Factors & Dimensional Analysis

Conversion factors are used to interchange units or measurements with fixed relationships.

• Conversion Factor: Expresses a fixed relationship as a fraction (e.g., $1\,\text{kg} = 1000\,\text{g}$, so $\frac{1000\,\text{g}}{1\,\text{kg}}$ or $\frac{1\,\text{kg}}{1000\,\text{g}}$).

• Dimensional Analysis: Write the conversion factor so that starting units cancel with the same units in the conversion factor.

• Example: How many 8.0 oz. patties can you make from 3.2 lbs. of hamburger?

  • $3.2\,\text{lbs} \times \frac{16\,\text{oz}}{1\,\text{lb}} \times \frac{1\,\text{patty}}{8.0\,\text{oz}} = 6.4\,\text{patties}$

Mass Percent as a Conversion Factor

Composition is often reported as mass percent, which can be used as a conversion factor in calculations.

• Example: A ring contains 32.5% Au by mass. Conversion factors: $\frac{32.5\,\text{g Au}}{100\,\text{g ring}}$ or $\frac{100\,\text{g ring}}{32.5\,\text{g Au}}$.

Interpreting Graphs

Graphs are used to visualize data and trends in chemistry.

• Read off (X,Y) pairs by selecting values on axes.

• Slope ($\Delta Y/\Delta X$) represents the rate of change.

Practice Problems

Throughout the chapter, practice questions are provided to reinforce concepts such as classification of matter, properties, significant figures, and unit conversions.

Additional info: These notes expand upon the original slides by providing full definitions, examples, and context for each concept, ensuring a self-contained study guide for General Chemistry students.